Half-eigenvalues and semilinear problems with jumping nonlinearities

17 May 2004
Bryan Rynne
We consider semilinear Sturm-Liouville and elliptic problems with jumping nonlinearities. We show how `half-eigenvalues' can be used to describe the solvability of such problems and consider the structure of the set of half-eigenvalues. It will be seen that for Sturm-Liouville problems the structure of this set can be considerably more complicated for periodic than for separated boundary conditions, while for elliptic partial differential operators only partial results are known about the structure in general.
  • Applied Analysis and Mechanics Seminar